A tunable dual-band terahertz sensor based on graphene is proposed. The sensor consists of a metal bottom layer, a middle dielectric layer, and single-layer graphene patterned with four strips on the top. The numerical simulations results show that the proposed sensor exhibits two significant absorption peaks at 2.58 THz and 6.07 THz. The corresponding absorption rates are as high as nearly 100% and 98%, respectively. The corresponding quality factor (Q) value is 11.8 at 2.58 THz and 29.6 at 6.07 THz. By adjusting the external electric field or chemical doping of graphene, the positions of the dual-frequency resonance peak can be dynamically tuned. The excitation of plasma resonance in graphene can illustrate the mechanism of the sensor. To verify the practical application of the device, the terahertz response of different kinds and different thicknesses of the analyte is investigated and analyzed. A phenomenon of obvious frequency shifts of the two resonance peaks can be observed. Therefore, the proposed sensor has great potential applications in terahertz fields, such as material characterization, medical diagnosis, and environmental monitoring.